Mathematics Colloquium: A Corporative Bond Model with Credit Rating Migration Risk

2016-08-25

4:10pm Neill 5W

Professor Jin Liang

In this talk, I will present a corporative bond model with credit rating migration risk. The mathematical model can be formulated as a free boundary problem associated with Black-Scholes type of equation. An asymptotic traveling wave solution for the model problem is established. This is the first study to associate the asymptotic traveling wave solution to the credit rating migration problem. The pricing problem with credit rating migration risk is modeled by a free boundary problem. The existence, uniqueness and regularity of the solution are obtained. Under some condition, we proved that the solution of our credit rating problem is convergent to a traveling wave solution, which has an explicit form. Furthermore, numerical examples are presented.

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